Section 2.2 Preferences and rationality
Consumer preferences lie at the core of consumer theory. Put simply, consumer preferences capture a decision maker’s ability to express a preference ranking over her available choices. These choices are typically consumption bundles: combinations of goods available to the decision maker. If the good under consideration is mountain bikes, then the consumption bundle can be represented with a single variable, such as \(x\text{.}\) A consumer having 2 mountain bikes could then be represented by \(x = 2\text{.}\) If there are multiple goods under consideration, such as slices of pizza and soft drinks, the consumption bundle would be a combination of slices and drinks represented by an ordered pair, like \((x, y)\text{.}\) Here, the ordered pair \((3, 1)\) indicates a consumer with 3 slices of pizza and 1 soft drink. Naturally, since any number of combinations can be imagined, \((4, 4)\text{,}\) \((2, 0)\text{,}\) and \((2, 1)\) all represent possible consumption bundles.
A consumer preferences expresses which of two consumption bundles a consumer ... prefers. If a consumer is faced with two options for bundles of pizza and drinks - bundle
\(a = (2, 1)\) and bundle
\(b = (3, 0)\)- she may prefer to consumer bundle
\(a\) to bundle
\(b\text{,}\) or the other way around. She may also value the bundles equally; in this case, we say she is
indifferent between bundle
\(a\) and bundle
\(b\text{.}\) 1 With realistically many available bundles, the consumer could feasibly construct a preference ranking across all available bundles, as shown below:
|
bundles |
|
|
| best |
\(a = (4, 3)\) |
|
\(d = (3, 1)\) |
|
\(c = (2, 2)\) |
|
\(f = (2, 1)\text{,}\) \(b = (0, 4)\)
|
| worst |
\(e = (0, 0)\) |
An example of a preference ranking.
Consumer preferences can vary greatly from person to person, but economists often consider several assumptions which may characterize those preferences. We begin with the assumptions of completeness and transitivity.
Assumption A1 (Completeness): The consumer can form a preference over (or be indifferent between) any two bundles.
Assumption A2 (Transitivity): If, for a consumer, bundle \(a\) is preferred to bundle \(b\text{,}\) and bundle \(b\) is preferred to bundle \(c\text{,}\) then this consumer must prefer bundle \(a\) to bundle \(c\text{.}\)
The assumption of completeness (A1) ensures that faced with any two alternatives, the consumer can always express a preference or indifference. In essence, completeness means the consumer can always make a choice! This, of course, maintain that a consumer can choose to express indifference and value the two alternatives the same. The assumption of transitivity (A2) describes a kind of internal consistency between the expressed preferences of the consumer.
Importantly, we can now formally discuss the concept of a rational consumer. In short, the notion of consumer rationality requires only assumptions A1 and A2 to be true. Rationality does not impose that consumers act selfishly, or that consumers prefer any particular types of bundles! Instead, it is much weaker, requiring only that consumers can (a) make choices and (b) do so with a minimal degree of internal consistency. Importantly, rationality is satisfied if the following two conditions are satisfied:
The consumer expresses preferences which satisfy A1 and A2.
From all available bundles, the consumer chooses her most preferred bundle.
2
Well-known economist Ariel Rubinstein frames this slightly differently in his book Economic Fables when describing how he presents the definition:
The rational man has preferences regarding the consequences that are likely to result from choosing various alternatives. When he is required to choose, he:
asks himself what alternatives he has;
clarifies to himself the consequence that would follow upon choosing each of the possible alternatives;
chooses the alternative that leads to the best consequence (as expressed in 2) in accordance with his preferences, from among all of the reasonable alternatives in the situation (as expressed in 1). (Rubenstein 44)
Rubenstein emphasizes two additional factors supporting rationality. First, he suggests that a rational decision maker should be able to identify what each of her available options (or bundles, or alternatives) is. Second, he suggests that a rational decision maker should be able to anticipate the consequence of choosing each of those options. Do you think these factors are reasonable additions to a definition of rationality? Are there instances where either would fail?
In Depth 2.2.1. Do units of goods need to be whole numbers?
For many examples of goods, it seems obvious to measure those goods using whole numbers. When \(x\) gives the number of mountain bikes a consumer may want to purchase, \(x = \frac{1}{2}\) doesn’t make much sense. Who would consider buying half a mountain bike? (Maybe someone who only wants it for parts?) Restricting our model to values of \(x = 1, 2, 3, \ldots\) makes sense.
But in many other examples, measuring quantity by whole number isn’t necessary or realistic. Apples, for one, are often sold by the pound: so a consumer buying 3 apples may actually be purchasing 1.4 pounds of apples. If prices are given by the pound, then our model should set the quantity of apples at \(x = 1.4\text{.}\) Or take gasoline! At the pump, we purchase gas by the gallon, but can purchase gasoline in quantities measured to several decimal places. Here, a consumer might consider purchasing \(x = 12.2754\) gallons of gasoline to fill her tank.
In some scenarios, whole numbers seem logical, while in others, we want to allow a consumer to consider non-whole number bundles. Rather than switch back and forth according to the good, however, it is a common convention not to restrict bundles to whole numbers in general. Models in consumer theory are a bit easier to solve when solutions can be non-whole numbers, so economists are typically willing to forgo the added realism of whole numbers for those examples (mountain bikes) where fractions may not make sense.
Key terms in this section:
consumer preferences
consumption bundle
ordered pair
indifference
completeness
transitivity
rational consumer
